I can't get an arrayed object to follow bezier curve
There are two things that cause trouble:

1. Array orientation (little trouble)
Your array is facing the wrong way.
Just rotate it like this and set the Relative offset on the X axis.  



2. Curve radius (big trouble)
The curve radius is set to 200 (waaay too high), which causes significant distortion.
Either change the curve radius to 1.
Or uncheck Radius in the curve properties.   

Change curve radius to 1.
Sidebar > Item > Mean Radius


Or disable radius influence altogether
Curve > Shape > Radius (uncheck).